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Line list of 12CH4 in the 4300–4600 cm–1 region
Andrei Nikitin, A.A. Rodina, X. Thomas, L. Manceron, L. Daumont, M. Rey, K. Sung, A.E. Protasevich, S.A. Tashkun, I.S. Chizhmakova, et al.
To cite this version:
Andrei Nikitin, A.A. Rodina, X. Thomas, L. Manceron, L. Daumont, et al.. Line list of 12CH4 in the 4300–4600 cm–1 region. Journal of Quantitative Spectroscopy and Radiative Transfer, Elsevier, 2020, 253, pp.107061. �10.1016/j.jqsrt.2020.107061�. �hal-03045996�
Line list of
12CH
4in the 4300-4600 cm
-1region
1 2
A.V. Nikitin1, A.A. Rodina1, X. Thomas2, L. Manceron3,4, L. Daumont2, M. Rey2, K. Sung5, 3
A.E. Protasevich1, S.A. Tashkun1, I. S. Chizhmakova6 Vl. G. Tyuterev2,7 4
5
1.V.E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences, 1, Akademichesky Avenue, 6
634055 Tomsk, Russian Federation
7 2.Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089, Université de Reims, 8
U.F.R. Sciences, B.P. 1039, 51687 Reims Cedex 2, France
9 3.AILES Beamline, Synchrotron SOLEIL, L’Orme des Merisiers, St-Aubin BP48, F-91192 Gif-sur- 10
Yvette Cedex,France.
11 4.Sorbonne Université, CNRS, MONARIS, UMR 8233, 4 place Jussieu, Paris, France
12 5.
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, 13
CA 91109, USA
14 6
Institute of Monitoring of Climatic and Ecological Systems, Russian Academy of Sciences , 10/3, 15
Academichesky avenue, 634055, Tomsk, Russian Federation 16
7 QUAMER,Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russian Federation 17
18 19 20 21
Number of Pages: 22 22
Number of Figures: 8 23
Number of Tables: 5 24
Number supplemental files: 1 25
26
Running Head: 12CH4 absorption in the 4300-4600 cm-1 range 27
Keywords: high resolution spectra; CH4; methane; Octad; long path FTIR, vibration-rotation 28
states; intensities; infrared absorption; effective Hamiltonian.
29 30
Correspondence should be addressed to:
31
Andrei V. Nikitin, 32
*Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, SB RAS, 33
1, Academician Zuev square, 634055, Tomsk, Russia 34
E-mail: [email protected] 35
Tel. +73822 – 491111, ext. 1260 36
37
Abstract 38
Four spectra of normal samples of CH4 in the 4300-4600 cm-1 region were recorded by 39
using a Fourier transform spectrometer in Reims, France at long paths (202 m, 602 m, 1604 m, 40
and 1804 m) and different pressures. Additional spectra of 12CH4 covering the same region were 41
obtained at 80-123 K, and 93 m path length at SOLEIL Synchrotron in Paris for different 42
pressures and were used to measure low-J lines. Line positions and intensities were retrieved by 43
non-linear least-squares curve-fitting procedures and analyzed using effective Hamiltonian and 44
effective dipole transition moment models. A new measured line list contains positions and 45
intensities for 14151 absorption features. Quantum assignments were made for more than 10304 46
transitions of 12CH4, which represent ~99% of the integrated line intensity observed in this 47
region. Some 1699 hot band transitions for (Dyad – Tetradecad) system were assigned. The 48
resulting list of lines is significantly more accurate than previous empirical compilations.
49
Positions of 8605 cold band transitions for (GS – Octad) system were fitted with an RMS 50
standard deviation of 0.0014 cm-1. The sum of observed intensities between 4300 and 4600 cm-1 51
fell within 8% of the predicted value from ab initio variational calculations reported in the 52
TheoReTS database (http://theorets.univ-reims.fr ; http://theorets.tsu.ru).
53
54 55
Highlights 56
57
1. 14151 line positions and intensities were retrieved in the 4300- 4600 cm-1 region.
58
2. More than 7000 new assignments were made in the region.
59
3. 8605 experimental line positions were modeled to 0.0014 cm-1. 60
4. 5402experimental line intensities at 296 K were modeled to 9.9% rms.
61 62 63
1. Introduction
64 65
The aim of the present work is to improve the line list and to extend the assignments of 66
weak and hot band transitions of 12CH4 in the 4300 - 4600 cm-1 region of the Octad [1][2] [3] [4]
67
[5]. The Octad band system (24 upper state vibrational sublevels) has been first studied by Hilico 68
et al. [1] who also considered some hot bands [6] [7] for lower polyads of methane. The Octad 69
assignments have been extended in Refs. [2] , [4] and a list of strong lines in the 4300-4600 cm-1 70
range for atmospheric applications has been published in Ref [8]. The present analysis is a 71
continuation of a series of works [4], [5] using Fourier Transform spectra with long optical paths 72
and represents a considerable improvement over previous works [1], [2].
73
Over decades, a better knowledge of methane infrared spectra has been demanded for 74
various atmospheric and astrophysical applications [9], [10], [11]. This task was motivated by 75
new challenges related to remote sensing of planetary atmospheres. Among them, many studies 76
have been focused on the study of radiative properties of the Titan atmosphere (Saturn's largest 77
satellite), which is composed of 98.6% nitrogen and 1.4% methane at temperatures ranging 78
between 70 K and 200 K [12] [13] [14] [15] [16] [17]. Reliable parameters of methane 79
absorption and emission bands are essential for accurate interpretation of the IR spectra provided 80
by orbiting and ground-based observatories [18], [19], [20], [21], [22]. The insufficient coverage 81
and accuracy of spectral data became a major issue for investigations of outer planets [23] [14]
82
[15]. Despite recent progress [3] [24] [25] [8] [26] [27] [4] [28] [5] in the methane modeling, 83
available line lists [29] [30] [31] [32] [33] [34] [35] based on laboratory measurements do not 84
yet provide all necessary information to reproduce atmospheric methane spectra in the near 85
infrared. This is particularly the case of relatively weak absorption bands that significantly 86
contribute to the absorption at long optical paths of planetary atmospheres [36].
87
Because of high tetrahedral symmetry, some normal modes of methane are doubly or 88
triply degenerate in the harmonic approximation and fall within nearby intervals. Additionally, 89
there are accidental resonances due to near coincidence of fundamental vibrational frequencies 90
and of their combinations ( 1 3 22 24) that results in grouping vibrational levels into 91
so-called polyads (Dyad, Pentad, Octad, etc…) [37]. The vibrational energy levels with the 92
same polyad number calculated from the four vibrational quantum 93
numbers fall within the same energy range. In this work, we study the methane spectra belonging 94
to the Octad band system with P=3. The scheme of 12CH4 vibrational states is shown in Figure 1.
95
The blown-up scale at the right-hand side represents the sub-band centers with their symmetry 96
types, which are studied in the present work.
97
At room temperature, our observed line positions and intensities agree with a series of 98
experimental lines reported in[2] [4] within experimental accuracy and could be well reproduced 99
by our theoretical model. However, in some intervals of the 12CH4 Octad , the calculated line 100
lists included in the databases [29] [30] cannot be used for modeling spectra at temperatures that 101
considerably differ from 296 K. In the nearby ranges 4600-4850 cm-1 and 3760-4100 cm-1 102
ranges, the accuracy of spectra modeling was considerably better than that in the 4100-4600 cm-1 103
range, which is the subject of the present work. Erratic behaviors of some line intensities at 104
temperatures other than room temperature could be due to incorrect quantum assignments of 105
experimental transitions in the past and to wrong lower level energy values. On the whole, in the 106
Tetradecad range, the linelist was recently composed and updated simultaneously with the 107
improved assignments [38] [39] [40]. This was not the case of the Octad range, where the list of 108
transitions had been compiled before high-accuracy effective models became available [2] [4]
109
[41]. A lot of observed line positions and intensities have been reported in Ref. [2], but the 110
authors did not aim at providing a complete list of the observed and assigned transitions.
111
Furthermore, the spectra of methane isotopologues and hot transitions of (Tetradecad – Dyad) 112
band system, which fall in the same range, had not been available at the time of previous 113
publications. Without this information, the full assignment of weak 12CH4 cold band transitions 114
was complicated. In the present work, we report an extensive list of assigned transitions in the 115
4300 - 4600 cm-1 range using experimental spectra recorded at various temperatures and path 116
lengths. This linelist provides a more accurate description of experimental spectra at room and 117
cold temperatures in comparison with currently available databases.
118 119
120
Fig. 1. Vibrational levels of the 12CH4 polyads (left side) and the vibrational sublevels of a 121
part of Octad (right side) corresponding to rovibrational bands analyzed in this work. The right 122
hand side panel displays the principal vibration quantum numbers (υ1υ2υ3υ), symmetry types of 123
vibration sublevels, and vibrational ranking numbers within the Octad. The symmetry types 124
correspond to irreducible representations of the Td point group [42] [37].
125 126
The paper is structured as follows. Experimental spectra recorded in GSMA (Reims) and 127
SOLEIL (Paris) at 100, 113, 123 and 290 K are described in Sections 2a and 2b. Section 3 is 128
devoted to the determination of line parameters and Section 4 to spectra assignments. Section 5 129
gives the information on newly assigned line lists provided in the Supplementary Materials.
130 131
2. Experiment
132 133
In this study, we used a large set of Fourier transform spectra (FTS) recorded in the GSMA 134
Laboratory at Reims University. Some of the spectra have already been presented in former 135
publications concerning specific studies [4, 43-45]. In the series of experimental studies, a 50 m 136
base multipass cell of GSMA has been optically configured to high-resolution step-by-step 137
spectrometer as first described in [4] [5] [43] [40] [44]. The absorption path lengths were set to 138
202, 602, 1603 meters by adjusting the number of the transverse beams inside the 50 meters 139
based White-type gas cell. The methane gas used to fill the cell is a natural abundance sample, 140
and the pressures varied from 1 to 25 Torr, as described in Table 1. The spectrometer is based on 141
the Connes principle and its apparatus function is mainly determined by the maximal optical path 142
difference (MOPD) and by the apperture chosen at the entrance of the spectrometer. During the 143
experiment, the average cell temperature was controlled with fluctuations in time that did not 144
exceed two degrees.
145
The first series of spectra with 1600 m absorption path-length in the 1.6 µm window of 146
methane (e.g., H-band) has been explored [45] for the Titan atmospheric spectra analysis [15]. In 147
this work, most of the measured lines were obtained from E, F, H, I spectra (see Table 1). G and 148
J spectra were only used to check the intensities of the weak lines. F and I spectra recorded at a 149
pressure of 5 Torr were used to determine the positions and check the intensities of the weak 150
lines in the 4300-4500 cm-1 range and to determine the positions and check the intensities of 151
some strong lines in the 4500-4600 cm-1 range. The spectra E and H were only used to check the 152
positions and intensities of the strongest lines in the region. Because of significant spatial 153
temperature grаdients within the cell for low-T conditions , the Reims spectra A, B, C were used 154
to determine positions of weak lines only at the initial stage of work.
155 156
157
Table 1. Experimental conditions for the series of CH4 spectra in the Octad range.
158
Spectrum ID
Iris Diameter, Focal length
(mm)
Pressure
(Torr) Temperature (K)
Absorption path
(m)
GSMA FTS spectra recorded in Reims
A
4.5, 1040
3.43 110 8.52
B 4.17 113 32.52
C 3.28 113 80.52
E
4, 1040
1.06 292
201.84
F 5.03 291
G 25.98 289
H
4, 1040
1.05 289
602.32
I 5.08 290
J 25.11 289
K
3.5, 1040 1.065 289
1603
L 4.070 288
SOLEIL FTS spectra recorded in Paris M
1.5, 418
0.0073
100 93.14
N 0.0019
O 0.00159
P 0.00155
Q 0.00068
R 0.00094 102
S 0.03 112
T 1.16 123
159
Six spectra were recorded at low temperature at Synchrotron SOLEIL using the long path 160
cryogenic cell described in reference [46] and the Bruker 125 HR interferometer. The optical 161
path length in the cell was set to 93.14(1) meters for all these recordings. Such a long path length 162
would make the strong lines in the region easily being saturated and subject to unwanted non- 163
linearity effects unless the sample pressure was used sufficiently low. At the low sample 164
pressure, however, the pressure readings of the cold cell become uncertain due to thermo- 165
molecular effects, especially when the pressure sensor is placed outside the cell, as was the case 166
for our setup. To avoid these possible issues, the methane sample was diluted in pure nitrogen 167
gas in a 3L container at a 0.100(1)% mixing ratio and precisely measurable amounts (0.917 to 168
2.52 mbar) were introduced in the cell [47]. The mixing ratio was chosen so that nitrogen 169
pressure broadening is not an issue here. The relative uncertainty on the methane pressure is 170
estimated to be about 1.5%. The spectra were recorded using a Si/CaF2 beamsplitter, a scanner 171
optical velocity of 5.06 cm/s, a low pass filter with 40 kHz cut-off and a 120 cm maximum 172
optical path difference. This corresponds to 0.0075 cm-1 resolution, according to Bruker‟s 173
definition, which is about the Doppler linewidth at this temperature. The spectra were obtained 174
with no apodization and 2400 scans were averaged for each of them. Wavenumber calibration 175
was carried out using both weak residual water lines and CO lines resulting from a special 176
spectrum recording. For this spectrum, a separate mixture containing 0.0053 torr of CO with a 177
trace amount of methane was used. For spectra M-Q, an agreement within 3% (1σ) for the CO 178
intensities available in HITRAN-2016 [29] was obtained. The average temperature was 179
measured in two ways: a value T= 100 ± 3 K was obtained using 12 different temperature 180
sensors along the optical path giving about 3 K uncertainty (1σ) [46]. Secondly, using the CO 2- 181
0 line intensities of the calibration spectrum, an average temperature of 99 ± 3K was obtained, 182
consistent with the sensor's direct temperature measurement. In the 4300-4600 cm-1 range, S and 183
T spectra recorded at 112 and 123 K were used to determine line positions and intensities for low 184
J values mostly for weak lines. The same setup as for spectra M-Q was used for spectra R-T.
185 186
3. Line parameters in the 4300 -4600 cm-1 region
187 188
All positions and intensities have been obtained using the SpectraPlot software [48] from 189
spectra recorded in Reims and Paris. All spectral features with intensities > 1.0×10-25 cm- 190
1/(molecule∙cm-2) and many of the lines with intensities between 1.0×10-25 and 2.0×10-26 cm- 191
1/(molecule∙cm-2) were retrieved. At the first stage, we used the same technique as described in 192
[40]. Line parameters of low J values were obtained from Spectrum S and T at 112 and 123 K, 193
respectively. Then, we used the fixed parameters determined from the low J lines to obtain the 194
parameters of strong lines from the spectra recorded with the optical path L = 201.84 meters. At 195
the next stage, we fitted weak lines using the spectra E, F, G, I, and J. The final fit was made 196
using the six room-temperature spectra E – J and spectrum T recorded at 123 K. In this case, 197
some positions of the low J lines were set to values previously obtained from cold spectra.
198
Calibration of spectra A, B, and C was carried out in the similar way as in Ref. [40]. The 199
previously observed methane lines and CO2 transitions were used to calibrate the spectra E, F, G, 200
H, I, and J. The CO transitions were used to calibrate the spectra K and L. For spectra A, B and 201
C, the calibration was checked for selected residual water transitions from the HITRAN-2016 202
database. The average shift of these transitions was 5.0 × 10-6 cm-1.When the spectra with 203
different pressures were used for a simultaneous fitting, the self-pressure-induced line shift 204
parameter was assumed to be the same for all lines equal to -0.013 cm-1/atm [49].
205
The strongest lines of 12CH4 (with intensities > 3.×10-23 cm-1/(molecule∙cm-2)) were almost 206
saturated in several spectra (1 Torr, 201 meters ) in the 4300-4600 cm-1 range. For these few 207
transitions the previously observed lines of Ref. [1] or HITRAN-2016 [29] values were 208
incorporated in our final line list. The corresponding 209 lines are flagged with H.
209
Some 8619 12CH4 transitions are now assigned in the 4300-4600 cm-1 region that is to 210
compare with 2834 experimental transitions assigned in Refs [2] [3]. Detailed examples of newly 211
measured and assigned transitions are shown in Figs. 2-4 for the 4308-4513 cm-1 region. A 212
comparison of observed and calculated spectra at 123 K using both the present work and 213
HITRAN-2016 [29] line lists is shown in Figs 5-6 for the 4338-4443 cm-1range. In these 214
examples, we compare new data with HITRAN-2016, which is the most frequently used 215
database for atmospheric applications, but the general conclusions are also valid for other 216
existing empirically fitted line lists. HITRAN-2016 spectroscopic database [29] contains 29009 217
transitions of 12CH4 in this range with the intensity cutoff 1×10-29 cm-1/(molecule∙cm-2), only 218
about 10% of these lines being measured and assigned in laboratory spectra [2] [3].
219
These comparisons show that HITRAN-2016 [29] provides correct integrated methane 220
absorption on the entire scale, but the line-by-line list fails to reproduce spectra at low 221
temperatures in the considered range under high resolution. It would not provide reliable 222
simulations of methane absorption for some spectral features when the temperature conditions 223
significantly differ from 296 K. Furthermore, Figure 7 illustrates that, in some cases, previously 224
available line lists inaccurately describe observed spectra in some intervals even at 296 K. As 225
many other empirical compilations, it comprised a mixture of quite accurate laboratory 226
measurements and extrapolations using the effective Hamiltonian and effective dipole moment 227
models. Figures 5 and 7 illustrate that HITRAN-2016 database (and other empirical compilations 228
as well) contains some transitions in this range, for which line positions and intensities have 229
significant errors beyond their reported uncertainties. This mostly concerns several series of 230
weak and medium lines with intensities in the range 3×10-23 - 1×10-24 cm-1/(molecule∙cm-2). An 231
invalid assignment of transitions could lead to errors in the temperature dependence and to 232
inaccurate interpretation of the observed transmittance in terrestrial and planetary atmospheric 233
for some spectral intervals.
234
A sample of seventeenisolated lines observed in this work (TW) with intensities in the range 235
[1×10-24 - 3×10-23] cm-1/(molecule∙cm-2) is listed in Table 2. The third column shows the 236
intensities ratio from HITRAN-2016 line list, ratioed to the corresponding intensities of this 237
work in the third column. The fourth column gives the ratio of ab initio line intensity to that 238
measured in this work. Initially, these theoretical predictions were obtained using ab initio 239
ACVQZ dipole moment surface [50] and global variational calculations [51] [52] [53] as 240
included in the TheoReTS information system [54]. Some lines listed in Table 2 were 241
considered „unstable‟ in terms of the classification described in Ref [55] due to sharp accidental 242
resonances. In the last column of Table 2, the corresponding outliers of variational calculations 243
were smoothed using accurate wavefunctions of the optimaised EH. Table 2 shows that the 244
intensities obtained in this work for the seventeen relatively strong lines listed are much closer to 245
the best available ab initio intensities [54] and 7% higher than those HITRAN-2016 [29] [1].
246
Table 2. Example of intensities for seventeen isolated lines in the 4300 - 4600 cm-1 region.
247 248
Line positiona
Line intensity This workb
Intensity ratio to TW HITRAN-2016 Ab initio c
4309.370639 15.61 0.86 0.98
4338.140149 6.999 0.54 0.99
4353.040613 17.28 1.06 0.88
4391.662283 4.798 0.93 0.91
4415.850673 15.57 0.59 0.96
4418.536734 19.12 0.86 1.00
4425.295494 18.67 0.83 0.98
4455.944122 63.21 1.20 1.06
4502.424255 62.86 1.00 1.01
4508.039449 22.22 0.96 0.98
4508.413075 41.06 0.98 1.02
4560.096669 2.887 0.74 1.05
4560.374781 21.53 1.28 0.97
4569.715772 16.46 0.99 1.00
4577.868249 46.67 1.08 1.04
4588.477338 13.37 0.98 1.02
4588.704137 11.74 0.96 0.97
Average ratio 0.93 0.99
Notes:
249
a wavenumber measured in this work [cm-1].
250
b intensity measured in this work in 10-24 cm-1/(molecule∙cm-2) 251 c
with corrected outliers of “unstable lines “ ( see the text ) 252
253
The integrated intensities (obtained by summation of intensities of all lines) in the range 4300- 254
4600 cm-1 are shown in Table 3. The integrated intensities of our observed line list are close to 255
the integrated intensities of HITRAN-2016 [29]. The integrated intensities of [54] and GEISA 256
[30] appear to be larger by 5-7% than those of this work. There are two factors contributing to 257
this difference: greater intensities of the strong and intermediately strong lines and much larger 258
number of weak lines incorperated in full variational calculations [54]. The average absolute 259
uncertainty of the intensities measured in this work is estimated as 5-10%. The factors 260
influencing the accuracy include temperature fluctuations of ~ 1.5 degrees and a large aperture of 261
3-5 mm for the Reims spectrum sets. Considerable numbers of transitions with intensities below 262
1 × 10-24 cm-1 / (molecule ∙ cm-2) are found to be blended, and an empirical determination of 263
transition intensity strongly depends on the neighboring lines. In many cases, the lower J was not 264
known, and a default lower state energy value of 814.6 cm-1 was used. Since the Reims spectra 265
were recorded at a temperature of T = 291 K, recalculation of the intensities of such transitions at 266
T = 296 K could be incorrect for the unassigned lines. Note, that the 113 K spectrum was 267
particularly useful for transitions blended by higher J lines in the room temperature spectra.
268
However, for more accurate measurement of intensities, further extension of assignments and 269
recording of spectra with a shorter optical path and better temperature stabilization is necessary.
270 271
Table 3. Integrated methane intensities in the range 4300-4600 cm-1 272
273
Source #lines S Int*
This work : observed intensities 14151 3.98***
This work : calculated from empirically fitted EDM model
24221 3.90
This work: calculated from ab initio based EDM intensities (EDM fitted to variational intensities [54] computed using ACVQZ dipole moment)
23812 4.21
Full variational ab initio based list [54] ** 286635 4.20 HITRAN-2016 [29] (12CH4 only) 29009 4.09
GEISA-2015 [30] 22127 4.18
* Sums of line intensities (10-19 cm/molecule) 274
** Ab initio intensities computed with ACVQZ DMS [55], see TheoReTS [54] including hot 275
bands (for natural 12CH4 abundance) 276
*** contains 13CH4
277
278
Fig. 2. Example of quantum number assignments in the 12CH4 spectra. The upper panel shows 279
residuals (obs-calc) for three spectra (orange 602 m at 289 K and green Reims 201 meter 280
spectra at 291 K, blue S, T cold spectra). Next panel below shows 602 meter (black) and two 281
calculated spectra (orange). Next panel below shows the 201 meter observed spectrum in black, 282
two calculated 201 m spectra (green). Next panel S, T shows observed spectra and two 283
corresponding calculated spectra. Next panel shows assigned experimental line sticks and the 284
lowest panel – our calculated intensity sticks at 296 K.
285 286
287
Fig. 3. The same as in Fig. 2, except for the spectral region of 4402.4-4403.4 cm-1 288
289
290
Fig. 4. The same as in Fig. 2, except for the spectral region of 4512-4514 cm-1. 291
292
293
Fig. 5. Comparison of two line lists at 123 K in the 4342 -4344 cm-1 range. Upper panel:
294
residuals (obs-calc) between HITRAN2016 and observed spectra (black) and residuals for 295
observed linelist of this work (red). Middle panel: observed spectra T (see Table2), Bottom 296
panel: simulation using experimental linelist of this work (red) and that of HITRAN2016 (black), 297
where some medium size lines are missing, for example, those at 4342.98 and 4343.55 cm-1. 298
299 300
301
Fig. 6. Comparison of two line lists at 123 K in the 4441-4443 cm-1 range. Upper panel: shows 302
residuals (obs-calc) for HITRAN2016 and observed spectra (black) and for observed linelist of 303
this work (red). Middle panel: observed spectra T (see Table2), Bottom below: observed linelist 304
of this work (red) and HITRAN2016 (black), showing the HITRAN intensities are substantially 305
306 off 307 308
309
Fig. 7. Comparison of the experimental line sticks with the calculated intensity sticks, as well as 310
with the HITRAN 2016 data at T=290 K. The upper panel shows HITRAN2016. The lower panel 311
shows the calculated intensity sticks. The next panel shows experimental line sticks and the 312
lowest panel – experimental spectra for 201 m (black) and calculated spectra for 201 m . 313
314
4. Spectra assignment
315 316
The line-by-line assignment of spectra relies on a comparison of calculated lists that contain 317
complete quantum identifications with observed spectra. Previous works on the assignment of 318
crowded methane spectra in the range of Octad [1] [9] have not been sufficiently complete to 319
cover transitions of all sub-bands.
320
The traditional approach for spectral analyses based on effective Hamiltonian (EH) and 321
effective dipole moment (EDM) models ( see for example [37] [56] [35] and refs therein) had 322
faced the well-known issues related to rapidly increasing number of adjustable parameters.
323
Thanks to improved ab initio calculations of the potential energy surfaces (PES) and of dipole 324
moment surfaces (DMS) [57], [50], [58], [59], [60], [61] and to global variational calculations 325
[51] [52] , a better understanding of absorption bands in spectra of methane isotopologues has 326
become posssible [54] [62] [63] [64] [65] . In particular, global theoretical line lists [17], [54]
327
for astrophysical applications [66] [67] [68] [69] [70] had been generated at various temperature 328
conditions from 50 K up to 3000 K. These theoretical studies cited above have permitted a 329
qualitative agreement of band intensities with experiments and an improvement of predictions 330
for the band centers [57] [60], however the accuracy of purely ab initio line positions is not yet 331
sufficient for high-resolution atmospheric applications.
332
A recent progress in methane spectra analyses [40] [71] [72] was due to a “combined 333
approach” [41] that comprised three steps. First, the ab initio based effective EH polyad models 334
were derived from the molecular PES via a high order Contact Transformation (CT) method 335
[41]. This provided realistic estimations for the coupling parameters between various 336
rovibrational bands and for related resonance perturbations in the observed spectra. Finally, a 337
fine tuning of a reduced set of empirically adjusted parameters permitted to extend the number of 338
assigned lines. The formalism of irreducible tensor operators (ITO) [42] [37], implemented in 339
the MIRS computational code [56], was used for a full account of tetrahedral symmetry 340
properties of the methane molecule.
341
A more detailed discussion can be found in refs [40] [71] [43] devoted to assignments of 342
different parts of the Tetradecad [43] [71] [72] in previous analyses. In this work, we used the 343
most recent EH of [40] obtained via the “combined approach” [41] as an initial model to extend 344
assignments in the present spectral range.
345 346 347 348 349 350 351 352 353 354 355 356
357 358 359 360 361 362
Table 4. Line position and intensity statistics for 12CH4 transitions at 296 K corresponding 363
to the studied range 364
Vibration upper state
levels, symmetry
Vibration Energy cm-1
This work
Calculated from PES Line positions Line intensities
Exact KEO* , Ref [73], PES [57]
CT # Ref [41], PES [74]
Number Fitted
lines
RMS
(10-3 cm-1) JMin JMax
Number Fitted Transit.
RMS %
(0003) F2 (0102) E (0102) F1 (0102) A1 (0102) F2 (0102 ) E (0102) A2 (1001) F2 (0011) F2 (0011) E (0011) F1 (0011) A1 (0201) F2 (0201) F1 (0201) F2 (1100) E (0110) F1 (0110) F2 (0300) E (0300) A2 (0300) A1
3870.485238 4101.391836 4128.763930 4132.863475 4142.861828 4151.202962 4161.840387 4223.460976 4319.208149 4322.188360 4322.590936 4322.691766 4348.718167 4363.607752 4378.948765 4435.125649 4537.550360 4543.760944 4592.036524 4595.278804 4595.515674
3870.506 4101.426 4128.744 4132.874 4142.810 4151.164 4161.793 4223.566 4318.958 4321.946 4322.351 4322.429 4348.742 4363.608 4378.943 4435.277 4537.353 4543.574 4592.117 4595.276 4595.544
3870.839 4102.026 4129.233 4133.553 4143.119 4151.558 4162.141 4223.569 4319.412 4322.485 4322.744 4323.024 4349.458 4364.108 4379.351 4435.232 4537.746 4544.081 4592.830 4595.667 4595.976
2 4 63 27 48 38 61 283 772 598 1090
449 744 653 693 750 998 1117
124 47 44
1.68 2.47 2.28 1.60 1.55 2.36 1.71 1.73 1.61 1.43 1.45 1.52 1.61 1.40 1.49 1.41 9.89 9.49 1.46 1.04 1.17
17 15
8 8 8 8 8 6 0 1 1 1 0 1 1 1 1 0 1 1 2
17 18 21 19 19 18 18 21 21 21 21 21 20 21 21 20 21 21 19 16 15
0 2 46 17 33 20 40 207 607 466 829 357 423 391 376 436 479 569 59 17 28
4.19 1.04 9.46 8.98 9.43 8.48 9.43 9.91 1.08 1.02 9.73 9.75 9.97 1.06 9.29 9.59 1.02 8.17 8.00 4.85
Total 8605 1.386 5402 9.9
Notes:
365
*) using exact kinetic energy operator (KEO) in internal curvilinear coordinates [73]
366 #)
using contact transformation (CT) method in normal coordinated [41]
367
368 369
In total, 886 EH parameters were adjusted to fit more than 34000 measured 12CH4 line 370
positions from the Dyad up to the lower edge of the Icosad range. It was necessary to include all 371
this data because the parameters of low lying polyads contribute to higher polyads according to 372
the EH polyad extrapolation scheme [37] [42] . Ten ground state 6th-order parameters were 373
fixed to the values of Ref. [75], and 62 parameters of the Dyad were empirically optimized. Of 374
the total number of symmetry-allowed 382, 1202, and 2539 EH 6th-order parameters specific to 375
the Pentad, Octad, and Tetradecad, only a restricted set of 211, 279, and 329 parameters were 376
adjusted. These samples of adjusted EH parameters correspond to the choise of our previous 377
works [40] [72] [44]. The major sets of remaining parameters were held fixed to the theoretical 378
predictions from the molecular PES via the CT method [41] . The obtained RMS (calculated – 379
observed) deviation for line positions 0.0014 cm-1 is closed to the average descrepancies of 380
combination differences for the upper level energy ~ 0.001cm-1, obtained using several 381
transitions . 382
383
5. The methane line list with assignments
384 385
In the Supplementary Materials of this work, we provide the line list compiled at 296 K, 386
including quantum assignments. Table 5 shows a sample of this list . It includes the observed 387
positions and intensities (at 296 K), the quantum assignments following the notations described 388
in Ref [40], and lower state energies. Self-broadening and air-broadening coefficients obtained 389
from Refs. [76] [77] were added to our final line list. More recent values of self-broadening and 390
air-broadening coefficients in the Octad region have also been obtained in Ref. [49] (see Refs.
391
[78] [79] [80] for the tetradecad region). Isotopic lines were identified using the line list of 13CH4
392
obtained from the spectrum of enriched 13CH4 [81] . 393
394
Table 5. Sample of Electronic Supplementary data. Methane at 296 K with assignments in the 395
3760-4100 cm-1 region.
396 397
Key
a
positions
0 (cm-1)b
Intensity cm-1 /(molec∙cm-
2)
Rotational assignmentd Elow
estimates (cm-1)e
Self HWf (cm-1/atm)
Air HWg (cm-1/atm) Lower state Upper state
+ 4300.310020 1.726e-24 0 11 F2 3 3 11 F1 84 690.017 0.069 0.0534 + 4300.320078 2.460e-25 0 16 F2 3 3 16 F1 126 1417.753 0.054 0.0316 + 4300.347522 6.940e-25 0 16 F2 4 3 16 F1 127 1418.137 0.054 0.0316 H 4300.365965 1.732e-21 0 3 A2 1 3 2 A1 8 62.878 0.079 0.0656
+ 4300.386978 1.892e-23 0 14 A1 1 3 14 A2 35 1095.828 0.061 0.0416 + 4300.390664 7.933e-25 0 16 F1 3 3 17 F2 76 1417.807 0.054 0.0316 - 4300.395409 2.357e-24 814.646 0.066 0.0499 + 4300.408638 5.657e-24 0 10 E 2 3 10 E 51 575.271 0.071 0.0565 + 4300.450200 3.049e-23 0 11 F2 2 3 11 F1 84 689.876 0.069 0.0534 + 4300.456513 2.247e-23 0 11 E 1 3 11 E 55 689.886 0.069 0.0534 H 4300.459438 1.063e-22 0 12 F1 2 3 12 F2 94 814.884 0.066 0.0499 + 4300.461964 3.824e-25 1 7 F2 4 4 7 F1 120 1631.804 0.076 0.0630 + 4300.501773 2.576e-24 1 3 A1 1 4 3 A2 17 1369.017 0.079 0.0657 + 4300.502860 1.440e-24 0 16 F1 2 3 16 F2 129 1417.129 0.054 0.0316 + 4300.310020 1.726e-24 0 11 F2 3 3 11 F1 84 690.017 0.069 0.0534 398
Notes:
399
a + assigned line, - unassigned line, 3 corresponds to 13CH4, H – line from HITRAN 400
b measured line positions.
401
c I(296 K): measured line intensities in cm/molecule.
402
d Lower and upper state rovibrational assignments are given by the vibrational polyad number P, the 403
rotational quantum number J, the rovibrational symmetry type C (Td irreducible representation) and the 404
rovibration ranking index α.
405
e Elow: recommended value for the lower state energy [in cm-1]. Order of priority: exact assignment, lower 406
J, observed E lower, default E lower corresponded to J=12 (see Text).
407
f Self-Broadening coefficient obtained from [76].
408
g Air-Broadening coefficient obtained from [77]
409 410
An overall comparison of 12CH4 line-stick diagrams in the considered spectral range 4300-4600 411
cm-1 from the three line list is shown in Fig. 8. This includes HITRAN2016 [29], experimental 412
list of the present work, and the ab initio born list of TheoReTS database [58] produced by 413
variational calculations. At this large scale of Fig. 8, all line lists look similar. However, the 414
detailed comparisons of observed and calculated spectra shown in Fig. 5 - 7 reveals considerable 415
differences for medium and weak lines between the HITRAN2016 list and this work.
416 417
418
Fig. 8 Line stick diagrams obtained from four line lists in the 4300-4600 cm-1 range. From top 419
downward: HITRAN2016; This work (observed line list); Variational calculations from 420
TheoReTS [54] based on ab initio dipole moment [55].
421 422
6. Conclusion
423 424
The main results of the present spectrum analysis in the 4300-4600 cm-1 region are the extended 425
assignments and improved line lists provided in the Supplementary Materials. More than 7000 426
new lines of 12CH4 up to J = 21 were assigned in experimental FTS spectra recorded at various 427
temperatures using a combined approach involving ab initio calculations with subsequent 428
empirical optimization of the effective model. Upper state energy levels were obtained using 429
empirical adjustment of a restricted subset of EH parameters, which were statistically well- 430
determined in the fit. This approach allowed us to find our several significant outliers in 431
available compilations of methane line lists in this range based on previous empirical 432
extrapolations. These results will permit including new assignments in a forthcoming updates of 433
HITRAN [29] and GEISA [30] spectroscopic databases.
434 435
Acknowledgments 436
The supports of the CNRS (France) in the frame of “Laboratoire International Associé SAMIA”, 437
of the French ANR project e-PYTHEAS (ref: ANR-16-CE31-0005), of the ROMEO computer 438
center Reims-Champagne-Ardenne and of Academic D.Mendeleev program of Tomsk State 439
